The fourth element: characteristics, modelling and electromagnetic theory of the memristor

In 2008, researchers at the Hewlett-Packard (HP) laboratories published a paper in Nature reporting the development of a new basic circuit element that completes the missing link between charge and flux linkage, which was postulated by Chua in 1971 (Chua 1971 IEEE Trans. Circuit Theory 18, 507-519 (doi: 10.1109/TCT.1971.1083337)). The HP memristor is based on a nanometre scale TiO2 thin film, containing a doped region and an undoped region. Further to proposed applications of memristors in artificial biological systems and non-volatile RAM, they also enable reconfigurable nanoelectronics. Moreover, memristors provide new paradigms in application-specific integrated circuits and field programmable gate arrays. A significant reduction in area with an unprecedented memory capacity and device density are the potential advantages of memristors for integrated circuits. This work reviews the memristor and provides mathematical and SPICE models for memristors. Insight into the memristor device is given via recalling the quasi-static expansion of Maxwell's equations. We also review Chua's arguments based on electromagnetic theory.